embedded_svc.settings.extraPrechatFormDetails can be used in Salesforce Embedded Service Chat to pass value to the Custom Field on the Chat Transcript object/entity.

Create a Custom Field in the Chat Transcript object to pass from Pre-Chat and store it on the record.

Custom Field:

Code Snippet:

        embedded_svc.settings.extraPrechatFormDetails = [ {
            "label": "Skill Selected",
            "value": "Sales",
            "transcriptFields":[ "Skill__c" ],
            "displayToAgent": true
        } ];

Output: